Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i,n) for(int i=0;i<n;i++)
int main(void){
    int n;cin>>n;
    vector<double>v(n);rep(i,n)cin>>v.at(i);
    sort(v.begin(),v.end());
    double ans=0;
    rep(i,n-3){ans=max(ans,(v.at(n-1)+v.at(n-2))/(v.at(i+1)-v.at(i)));}
    ans=max(ans,(v.at(n-4)+v.at(n-1))/(v.at(n-2)-v.at(n-3)));
    ans=max(ans,(v.at(n-4)+v.at(n-3))/(v.at(n-1)-v.at(n-2)));
    cout << fixed << setprecision(10);
    cout<<ans<<endl;
}